ME 221 Statics
Lecture #8
Sections 2.9 & 2.10
ME 221
Lecture 8
1
Homework
• Due Monday, January 27
– Chapter 2 problems:
– 61, 64, 70, 71, 72, 82, 86, 94, 105 & 113
• Grades posted in Blackboard
– HW #1 & Quiz #1 (and solutions)
– HW #2 & Quiz #2 soon (solutions posted)
– HW #3 solutions to be posted late Monday
ME 221
Lecture 8
2
Exam 1
• Wednesday, January 29
ME 221
Lecture 8
3
Particle Equilibrium
• For a particle to be in equilibrium, the
resultant of the forces acting on it must sum
to zero.
• This is essentially Newton’s second law
with the acceleration being zero.
• In equation form: SF = 0
ME 221
Lecture 8
4
Representing Equilibrium
F3
F2
F3
F4
mi
F1
F1
F4
R = F1 + F2 + F3 + F4 =0
ME 221
F2
Vector Diagram
Lecture 8
Vector Equation
5
Representing Equilibrium
 F1x   F2 x   F3 x   F4 x  0
          Matrix Form
 F1 y    F2 y    F3 y    F4 y   0
 F   F   F   F  0 
 1z   2 z   3 z   4 z   
F1x  F2 x  F3 x  F4 x  0
x-components
F1 y  F2 y  F3 y  F4 y  0
y-components
F1z  F2 z  F3 z  F4 z  0
z-components
ME 221
Lecture 8
Component
Form
6
Statically Determinate
• For 3-D equilibrium, there are three scalar
equations: SFx = 0 , SFy = 0 , SFz = 0
• Problems with more than three unknowns
cannot be solved without more information,
and such problems are called statically
indeterminate.
ME 221
Lecture 8
7
Free-body Diagram
A free-body diagram is a pictorial
representation of the equation SF = 0 and
has:
– all of the forces represented in their proper
sense and location
– indication of the coordinate axes used in
applying SF = 0
ME 221
Lecture 8
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ME 221
Lecture 8
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ME 221 Exam 1 Topics
•All of Chapters 1 & 2 except 2.11 Springs
•Newton’s Laws
•Units
•Scalars & vectors; defining, adding, etc.
•Laws of sine & cosine
•Resolution of a vector into components
•3D coordinates & unit base vectors
ME 221
Lecture 8
10
Exam 1 Topics
continued
•Directional cosines
•Components of a vector in nonorthogonal
terms
•Scalar products of two vectors
•2-D and 3-D equilibrium problems
•draw a good free-body diagram
ME 221
Lecture 8
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ME 221
Lecture 8
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